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Fourier Series of modulus[t] - example of this?

  1. Mar 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Does anyone know of a website, or a book, where I can see a worked example of the Fourier Series

    f(t) = [t]
    -∏<t<∏
    T=2∏

    Finding a0 and an

    Of course, it doesn't have to be t, it could be x or any other variable.

    Thank you.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 3, 2012 #2
  4. Mar 4, 2012 #3

    OldEngr63

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    Gold Member

    You have defined the function as
    f(t) = [t]
    -∏<t<∏
    T=2∏
    but that is not the example that you show worked out. The example that you show worked out is this one
    f(t) = |t|
    -∏<t<∏
    T=2∏
    This difference being that, in the latter case, the function between - π and +π is the absolute value of t; in the original problem statement, as you gave it, [t] is not really a well defined function.

    The absolute value function is an even function, so when we proceed to evaluate the coefficients for the Fourier series, the first one works out as

    ao = [itex]\frac{1}{2π}[/itex]∫π f(t) dt
    = [itex]\frac{1}{π}[/itex]∫0π t dt
    =[itex]\frac{π}{2}[/itex]

    The others follow in the usual fashion with the cosine multiplication.
     
  5. Mar 5, 2012 #4

    vela

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    Staff Emeritus
    Science Advisor
    Homework Helper
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    That should be either n or k, not both, in your equation. Let's just use n.

    What does the result of the integration give you when you assume n is odd and n is even?
     
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